Concerning about the computation of roots of a
quaternionic polynomial, the first numerically working algorithm to
find a root was presented by Ser\(\hat{o}\) dio, Pereira, and
Vit\(\acute{o}\) ria [1]}, and further contributions were made by
Ser\(\hat{o}\) dio and Siu [2]}, Pumpl\(\ddot{u}\) n and Walcher
[3]}, De Leo, Ducati, and Leonardi [4]}, Gentili and
Struppa [5]}, Gentili, Struppa, and Vlacci [6]}, Gentili
and Stoppato [7]}. A large bibliography on quaternions in
general was given by Gsponer and Hurni in 2006 [8]}. Recently,
Janovsk\(\acute{a}\)  and Opfer presented a method in [9]} for
producing all zeros of a simple quaternionic polynomial, by using
the real companion polynomial introduced for the first time by
Niven [10]}, the number one introduced in [11]}, and the
presentation of the powers of a quaternion as a real, linear
combination of the quaternion. Let us recall some notions first.
